Various series expansions for the bilayer S=1/2 Heisenberg antiferromagnet

TL;DR

This paper develops various series expansions to analyze the thermodynamic and ground-state properties of the bilayer S=1/2 Heisenberg antiferromagnet, providing insights into phase transition points and excitation spectra.

Contribution

It introduces multiple series expansion methods for the bilayer Heisenberg antiferromagnet, including high temperature, Ising, and dimer expansions, to study different phases and properties.

Findings

Transition point at (J2/J1)_c=2.537(5)

Estimated J2/J1 ratio for YBa2Cu3O6.2 is about 0.07

Computed excitation spectra and spin-wave properties

Abstract

Various series expansions have been developed for the two-layer, S=1/2, square lattice Heisenberg antiferromagnet. High temperature expansions are used to calculate the temperature dependence of the susceptibility and specific heat. At T=0, Ising expansions are used to study the properties of the N\'{e}el-ordered phase, while dimer expansions are used to calculate the ground-state properties and excitation spectra of the magnetically disordered phase. The antiferromagnetic order-disorder transition point is determined to be $(J_2/J_1)_c=2.537(5)$. Quantities computed include the staggered magnetization, the susceptibility, the triplet spin-wave excitation spectra, the spin-wave velocity, and the spin-wave stiffness. We also estimates that the ratio of the intra- and inter-layer exchange constants to be $J_2/J_1\simeq 0.07$ for cuprate superconductor $YBa_2Cu_3O_{6.2}$.